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Cellular automata (CA) are dynamical systems on symbolic configurations on the lattice. They are also used as models of massively parallel computers. As dynamical systems, one would like to understand the effect of small random…
By using quantum mechanical effects, quantum computers promise significant speedups in solving problems intractable for conventional computers. However, despite recent progress they remain limited in scaling and availability-making quantum…
By the progressive scaling of the feature size and power consumption in VLSI chips the part of energy dissipated due to information loss in irreversible computations will become a serious limitation in the near future. Quantum-dot cellular…
We construct a cellular automaton (CA) model that describes the movement of a particle in a disordered system. The mathematical properties of the CA model were examined by varying the configuration of grid and determining the number of…
We study the class of asynchronous non-uniform cellular automata (ANUCA) over an arbitrary group universe with multiple local transition rules. We introduce the notion of stable injectivity, stable reversibility, stable post-surjectivity…
In this paper we present the impact of classical electronics constraints on a solid-state quantum dot logical qubit architecture. Constraints due to routing density, bandwidth allocation, signal timing, and thermally aware placement of…
Quantum cellular automata (QCAs) are automorphisms of tensor product algebras that preserve locality, with local quantum circuits as a simple example. We study approximate QCAs, where the locality condition is only satisfied up to a small…
Finding a quantum battery model that displays a genuine quantum advantage, while being prone to experimental fabrication, is an extremely challenging task. In this Letter we propose a deceptively simple quantum battery model that displays a…
Cellular automata (CAs) and convolutional neural networks (CNNs) are closely related due to the local nature of information processing. The connection between these topics is beneficial to both related fields, for conceptual as well as…
While the ability to build quantum computers is improving dramatically, developing quantum algorithms is limited and relies on human insight and ingenuity. Although a number of quantum programming languages have been developed, it is…
In this paper we identify full list of Elementary Cellular Automata rules which can be simulated using a quantum circuit (there are 22 such rules). For every such rule we present quantum circuit implementing it with $O(N)$ gates.
A simple mechanism for the emergence of complexity in cellular automata out of predictable dynamics is described. This leads to unfold the concept of conditional predictability for systems whose trajectory can only be piecewise known. The…
This paper introduces a simple formalism for dealing with deterministic, non- deterministic and stochastic cellular automata in an unified and composable manner. This formalism allows for local probabilistic correlations, a feature which is…
In this paper we study the family of freezing cellular automata (FCA) in the context of asynchronous updating schemes. A cellular automaton is called freezing if there exists an order of its states, and the transitions are only allowed to…
Cellular automata (CAs) are fully-discrete dynamical models that have received much attention due to the fact that their relatively simple setup can nonetheless express highly complex phenomena. Despite the model's theoretical maturity and…
Quantum simulation can be implemented in pure digital or analog ways, each with their pros and cons. By taking advantage of the universality of a digital route and the efficiency of analog simulation, hybrid digital-analog approaches can…
Recent advances on quantum foundations achieved the derivation of free quantum field theory from general principles, without referring to mechanical notions and relativistic invariance. From the aforementioned principles a quantum cellular…
While there has been a keen interest in studying computation at the edge of chaos for dynamical systems undergoing a phase transition, this has come under question for cellular automata. We show that for continuously deformed cellular…
Quantum annealing (QA) is a heuristic algorithm for finding low-energy configurations of a system, with applications in optimization, machine learning, and quantum simulation. Up to now, all implementations of QA have been limited to qubits…
This work studies some aspects of the computational power of fully asynchronous cellular automata (ACA). We deal with some notions of simulation between ACA and Turing Machines. In particular, we characterize the updating sequences…